of Is in row i of this matrix is However this does not take into account the PageRank of the the rank of these sites, the higher the rank of site i. One approach for the connectivity matrix. In most cases the entries of x can be site corresponds to an entry of x, so the sum of the entries of sites the rank of site i. In fact, Google chooses the PageRank of a site s Exercises for 3.3 Exercise 3.3.1 In each case find the characteristic poly- nomial, eigenvalues, eigenvectors, and (if possible) an in- vertible matrix P such that P-¹AP is diagonal. a. A = c. A = e. A = g. A = i. A = 1 2 3 2 70-4 05 0 5 0 -2 -2 1 2 1 3 6-6 2 -1 ● 3 -4-2 1 1 -5 2 2 5 b. A = d. A = f. A = h. A = 2 0 0 Ο λ 0,2 μ 0 Ο μ 2 41 1 1 2 0 1 -1 010 301 200 -3 6 5 2 1 1 0 10 1 -1 2 Vk+1 = Avk f ing Theorem a. A = b. A = c. A = d. A = [ Exercise 3.3.3 if and only if A Exercise 3.3.4 A₁ = A -al, a Consider a linear dynamical system A if and only if Exercise 3.3.2 13 For more on PageRank, visit https://en.wikipedia.org/wiki/PageRank. 14See the articles "Searching the web with eigenvectors" by Herbert S. Wilf, L and "The worlds largest matrix computation: Google's PageRank is an eigenvecte

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer Exercise 3.3.21 c)
this context). Thus a large number of Is in row i of this matrix is
However this does not take into account the PageRank of the
the rank of these sites, the higher the rank of site i. One approach
for the connectivity matrix. In most cases the entries of x can be
site corresponds to an entry of x, so the sum of the entries of sites
the rank of site i. In fact, Google chooses the PageRank of a site s
Exercises for 3.3
Exercise 3.3.1 In each case find the characteristic poly-
nomial, eigenvalues, eigenvectors, and (if possible) an in-
vertible matrix P such that P-¹AP is diagonal.
a. A =
C. A =
e. A =
g. A=
1
3
i. A =
22
1
2
1
—
70-4
05
0
5 0 -2
-2 3
6 -6
2-1
1 1
-5
2 2 5
3
-4-2
0 0
λ
Ο λ 0
0
Ο μ
b. A =
d. A =
f. A =
h. A =
[
|,λαμ
- 1
1
2
1
2
2
0
1
-4
1
0
-1
01 0
301
200
-3
6
5
1
1
10
-1 2
Vk+1 = Avk f
ing Theorem
a. A =
b. A =
c. A =
d. A =
Exercise 3.3.3
if and only if A
Exercise 3.3.4
A₁ = A -al, a
Exercise 3.3.2 Consider a linear dynamical system A if and only if
13 For more on PageRank, visit https://en.wikipedia.org/wiki/PageRank.
14See the articles "Searching the web with eigenvectors" by Herbert S. Wilf, L
and "The worlds largest matrix computation: Google's PageRank is an eigenvecte
Moler, Matlab News and Notes, October 2002, pages 12-13.
L
Transcribed Image Text:this context). Thus a large number of Is in row i of this matrix is However this does not take into account the PageRank of the the rank of these sites, the higher the rank of site i. One approach for the connectivity matrix. In most cases the entries of x can be site corresponds to an entry of x, so the sum of the entries of sites the rank of site i. In fact, Google chooses the PageRank of a site s Exercises for 3.3 Exercise 3.3.1 In each case find the characteristic poly- nomial, eigenvalues, eigenvectors, and (if possible) an in- vertible matrix P such that P-¹AP is diagonal. a. A = C. A = e. A = g. A= 1 3 i. A = 22 1 2 1 — 70-4 05 0 5 0 -2 -2 3 6 -6 2-1 1 1 -5 2 2 5 3 -4-2 0 0 λ Ο λ 0 0 Ο μ b. A = d. A = f. A = h. A = [ |,λαμ - 1 1 2 1 2 2 0 1 -4 1 0 -1 01 0 301 200 -3 6 5 1 1 10 -1 2 Vk+1 = Avk f ing Theorem a. A = b. A = c. A = d. A = Exercise 3.3.3 if and only if A Exercise 3.3.4 A₁ = A -al, a Exercise 3.3.2 Consider a linear dynamical system A if and only if 13 For more on PageRank, visit https://en.wikipedia.org/wiki/PageRank. 14See the articles "Searching the web with eigenvectors" by Herbert S. Wilf, L and "The worlds largest matrix computation: Google's PageRank is an eigenvecte Moler, Matlab News and Notes, October 2002, pages 12-13. L
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